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Attractors of partial differential evolution equations in an unbounded domain

Published online by Cambridge University Press:  14 November 2011

A. V. Babin  and
M. I. Vishik
A. V. Babin
Affiliation:
MIIT, Obrazcova 15, 101475 Moscow, U.S.S.R.
M. I. Vishik
Affiliation:
Moscow State University, Mech.-Matem, Fac., 119899 Moscow, U.S.S.R.
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Synopsis

There is a large number of papers in which attractors of parabolic reaction-diffusion equations in bounded domains are investigated. In this paper, these equations are considered in the whole unbounded space, and a theory of attractors of such equations is built. While investigating these equations, specific difficulties arise connected with the noncompactness of operators, with the continuity of their spectra, etc. Therefore some new conditions on nonlinear terms arise. In this paper weighted spaces are widely applied. An important feature of this problem is worth mentioning: namely, properties of semigroups corresponding to equations with solutions in spaces of growing and of decreasing functions essentially differ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 3-4 , 1990 , pp. 221 - 243
Copyright
Copyright © Royal Society of Edinburgh 1990

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